The structure, the state of interfaces and magnetoresistance of [Co(1.5nm)/Cu(0.9nm)]n superlattices have been studied. The magnetoresistance decreases with the growth of n from 38% for n = 10 to 24% for n = 40. TEM studies have shown that the films have nanocrystalline structure with crystallites size 25 nm. The decomposition of the NMR spectrum I of a films in the constituents corresponding to the signals of 59Co atoms with different neighborhood is performed. The peak of I0 intensity characterizes Co atoms located inside the cobalt layer. The I1 and I2 peaks correspond to configurations in which there is, respectively, 1 or 2 Cu atoms in the nearest neighborhood of 59Co. The I3 peak characterizes the 59Co atoms of an “ideal” Co/Cu interface, coinciding with the close-packed <111> plane, in which every 59Co has three nearest neighbors of Cu atoms. It is obvious that the ratio of the intensities sum (I1 + I2 + I3) = Ii to I0 directly characterizes the perfection of interlayer interfaces. It is evident from the results obtained that the growth of perfection of Co/Cu interlayer interfaces with the addition of new layers is accompanied with the magnetoresistance decreasing.